Linear overdetermined boundary value problems in Hilbert space

We use the reproducing kernel Hilbert space method to solve the fifth-order boundary value problems. The exact solution to the fifth-order boundary value problems is obtained in reproducing kernel space. The approximate solution is given by using an iterative method and the finite section method. The present method reveals to be more effective and convenient compared with the other methods.

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Boundary value problems for nonlinear systems with generalized second-order differences

Carpathian Journal of Mathematics ◽

10.37193/cjm.2011.01.06 ◽

2011 ◽

Vol 27 (1) ◽

pp. 95-104

Author(s):

RODICA LUCA ◽

Keyword(s):

Boundary Condition ◽

Hilbert Space ◽

Nonlinear Systems ◽

Boundary Value Problems ◽

Existence And Uniqueness ◽

Real Hilbert Space ◽

Boundary Value ◽

Monotone Operators ◽

Second Order ◽

Differential Systems

In a real Hilbert space, we investigate the existence and uniqueness of the solutions for two classes of infinite nonlinear systems with generalized second-order differences, one of them subject to a boundary condition. Some applications to nonlinear differential systems with monotone operators are also presented.

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An algorithm for solving generalized algebraic Lyapunov equations in Hilbert space, applications to boundary value problems

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500006611 ◽

1988 ◽

Vol 31 (1) ◽

pp. 99-105 ◽

Cited By ~ 4

Author(s):

Lucas Jódar

Keyword(s):

Hilbert Space ◽

Boundary Value Problem ◽

Boundary Value Problems ◽

Operator Equation ◽

Boundary Value ◽

Linear Operators ◽

Bounded Linear Operators ◽

Space Applications ◽

Bounded Linear ◽

Image Position

Let L(H) be the algebra of all bounded linear operators on a separable complex Hubert space H. In a recent paper [7], explicit expressions for solutions of a boundary value problem in the Hubert space H, of the typeare given in terms of solutions of an algebraic operator equation

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Direct Computation of Operational Matrices for Polynomial Bases

Mathematical Problems in Engineering ◽

10.1155/2010/139198 ◽

2010 ◽

Vol 2010 ◽

pp. 1-12 ◽

Cited By ~ 6

Author(s):

Osvaldo Guimarães ◽

José Roberto C. Piqueira ◽

Marcio Lobo Netto

Keyword(s):

Hilbert Space ◽

Numerical Methods ◽

Boundary Value Problems ◽

Boundary Value ◽

Operational Matrices ◽

Direct Computation ◽

Linear Operation ◽

Matrix Operations ◽

Polynomial Bases ◽

Reference Matrix

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

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